CN102426690A - Method for secretly sharing and restoring digital image - Google Patents

Abstract

The invention discloses a method for secretly sharing and restoring digital images, which comprises the following steps of: (1) constructing an RS (Reed-solomon) delete code generator matrix G(k+n)*k; (2) initializing n sets of v1, v2, ^ and vn, and meanwhile, endowing a unique number di=I to the set vi, wherein i is more than or equal to 1 and less than or equal to n; (3) in a certain sequence, successively taking k pixel points which are not subjected to sharing operation from a secrete image S, and recording as alpha k*1=(a1, a2, ^, ak) gamma; (4) generating a matrix G(k+n)*k by the RS delete code to code the alpha k*1, and obtaining a code word beta, wherein beta (k+n)*1=(G(k+n)*k.alpha k*1)mod 251; (5) successively putting the last n elements (bk+1, bk+2, ^ and bk+n) in the generated code word vector beta into the sets of v1, v2, ^ and vn in sequence; (6) judging whether all pixel points in the secret image S are processed or not; if yes, entering step (7), and otherwise returning to the step (3); and (7) randomly selecting n images to serve as cover images, and respectively embedding data in the sets of v1, v2, ^ and vn into n cover images to obtain final n shadow images Y1, Y2, ^ and Yn. Compared with the prior art, the method disclosed by the invention has low computational complexity, and the use ratio of storage and transmission is effectively improved.

Description

A kind of digital picture secret sharing and restoration methods

Technical field

The present invention relates to image information concealing technology field, particularly relate to a kind of digital picture secret sharing and restoration methods.

Background technology

Compare the numerical information of many other types; Digital picture becomes the important means of expressing information in the network because of its characteristics such as lively, directly perceived; Possibly comprise in the image and a large amount of relate to safe sensitive information and can not directly transmit, need carry out just preventing after the encryption leakage of secret information these information.Can protect the validity of digital picture, assurance not to be intercepted and captured and distort through image secret sharing scheme through the information of Digital Image Transmission.(specifically see Chang-Chou Lin by Taiwan's scholars Chang-Chou Lin and Wen-Hsiang Tsai; Wen-Hsiang Tsai.Seeret image sharing with steganography and authentication [J] .The Journal of system and software; 2004 (73): a kind of digital picture secret sharing scheme that 405-414) proposes; This scheme has realized the (k of gray level image; N) thresholding, but this scheme can not accurately be recovered Secret Image and in storage and transmission, all exist great waste.

Summary of the invention

To the problem that prior art exists, fundamental purpose of the present invention is to provide a kind of digital picture secret sharing and restoration methods, only need obtain the shadow image that wherein is partially submerged into Secret Image and can accurately recover Secret Image file originally.

For realizing above-mentioned purpose, the invention provides a kind of embodiment of digital picture secret sharing method, Secret Image is broken to cover in the image, this digital picture secret sharing method comprises the steps:

(1) according to the k of image secret sharing thresholding, n value, the structure RS generator matrix G that deletes code _{(k+n) * k}

(2) initialization n set v ₁, v ₂, Λ, v _n, give set v simultaneously _iA unique numbering d _i=i, wherein 1≤i≤n;

(3) from Secret Image S, take out k successively in a certain order and share the pixel of operation, note is made α _{K * 1}=(a ₁, a ₂, Λ, a _k) ^Γ

(4) utilize the RS generator matrix G that deletes code _{(k+n) * k}To α _{K * 1}Carry out encoding operation, can obtain code word β, β _{(k+n) * 1}=(G _{(k+n) * k}α _{K * 1}) mod 251;

(5) with last n element (b among the codeword vector β that produces _K+1, b _K+2, Λ, b _K+n) put into successively in order and gather v ₁, v ₂, Λ, v _nIn;

(6) judge whether all pixels among the Secret Image S all dispose, if, then get into step (7), otherwise, step (3) returned;

(7) choose n width of cloth image arbitrarily as covering image, will gather v ₁, v ₂, Λ, v _nIn data be embedded into the n width of cloth respectively and cover in the image, obtain final n width of cloth shadow image Y ₁, Y ₂, Λ, Y _n

The generator matrix G that deletes code of the RS in the step (1) wherein _{(k+n) * k}Preceding k behavior one unit matrix, back n behavior one vandermonde determinant.

Step (3) can behavior be taken out the individual pixel of operation of sharing of k in proper order or to classify order as successively from Secret Image S.And when number deficiency k of the pixel of sharing operation among the Secret Image S, supply by 0.

In addition, the n width of cloth chosen of step (7) is covered image and Secret Image S has same type and size.The last d position of the n width of cloth being covered each pixel value of image hollows out, and wherein d=8/k then rounds up when d is non-integer, forms d position default map, will gather v ₁, v ₂, Λ, v _nIn data be embedded into the n width of cloth respectively and cover the default part of image.

After step (7) forms n width of cloth shadow image, can former Secret Image file be destroyed.

After using above-mentioned digital picture secret sharing method to share Secret Image; The present invention also provides a kind of secret restoration methods of digital picture that the Secret Image of sharing is recovered; This Secret Image forms the shadow image after embedding and covering image; Use at least k shadow image can recover the former Secret Image of sharing (when the quantity of shadow image then can not recover the former Secret Image of sharing during less than k), 2≤k≤n wherein, the secret restoration methods of this digital picture comprises the steps:

(1) S set of a sky of structure;

(2) from k width of cloth shadow image, extract original share data, constitute the k data sets, note is made v ' ₁, v ' ₂, Λ, v ' _k, will gather v ' ₁, v ' ₂, Λ, v ' _kNumbering note make d ' ₁, d ' ₂, Λ, d ' _k

(3) with data acquisition v ' ₁, v ' ₂, Λ, v ' _kArrange according to numbering order from small to large, the share data note after arranging is again made v ₁, v ₂, Λ, v _k, the corresponding numbering note in ordering back is made d ₁, d ₂, Λ, d _k

(4) matrix D of structure ' _{K * k}, with the delete code d of generator matrix G of RS _iThe row assignment is given D ' _{K * k}I capable, 1≤i≤n wherein;

(5) with matrix D ' _{K * k}Carry out 251 modular arithmetic after inverting and obtain check matrix D _{K * k}

(6) respectively from each share data acquisition v ₁, v ₂, Λ, v _kIn take out a numerical value in order, arrange to constitute vectorial β according to the order of sequence _{K * 1}=(b ₁, b ₂, Λ, b _k);

(7) α=(D β) mod 251, note is made α _{K * 1}=(a ₁, a ₂, Λ, a _k);

K element (a among the vectorial α that (8) will calculate ₁, a ₂, Λ, a _k) put into S set in order;

(9) judge share data acquisition v ₁, v ₂, Λ, v _kIn all data whether all dispose, if, then get into step (10), if not, then return step (6);

(10) the former Secret Image file shared of S set for recovering to obtain.

The present invention is with respect to prior art; Secret Image to be shared is passed through certain computing of sharing; To share Secret Image after the computing and be stored in n respectively and cover in the image, only need obtain wherein the Secret Image file that k shadow image can recover script fully.And this method computation complexity is low, effectively raises the utilization factor of storage and transmission.

Description of drawings

Fig. 1 is the process flow diagram of the embodiment of digital picture secret sharing method of the present invention

Fig. 2 is the process flow diagram of the embodiment of the secret restoration methods of digital picture of the present invention

Embodiment

Below in conjunction with accompanying drawing, specify embodiment of the present invention.

Specify digital picture secret sharing method of the present invention below in conjunction with Fig. 1.Fig. 1 is the process flow diagram of the embodiment of digital picture secret sharing method of the present invention.This digital picture secret sharing method comprises the steps:

S11, according to the k of image secret sharing thresholding, n value, the structure RS generator matrix G that deletes code _{(k+n) * k}, the RS generator matrix G that deletes code _{(k+n) * k}Preceding k behavior one unit matrix, back n behavior one vandermonde determinant,

$G_{(k+n)\×k}=\left(\begin{array}{ccccc}1& 0& 0& \mathrm{\Λ}& 0\\ 0& 1& 0& \mathrm{\Λ}& 0\\ M& M& M& O& M\\ 0& 0& 0& \mathrm{\Λ}& 1\\ d_{k+\mathrm{1,1}}& d_{k+\mathrm{1,2}}& d_{k+\mathrm{1,3}}& \mathrm{\Λ}& d_{k+1,k}\\ d_{k+\mathrm{2,1}}& d_{k+\mathrm{2,2}}& d_{k+2,3}& \mathrm{\Λ}& d_{k+\mathrm{2,4}}\\ M& M& M& O& M\\ d_{k+n,1}& d_{k+n,2}& d_{k+n,3}& \mathrm{\Λ}& d_{k+n,k}\end{array}\right);$

S12, an initialization n set v ₁, v ₂, Λ, v _n, be about to this n set v ₁, v ₂, Λ, v _nAssignment is empty, gives set v simultaneously _iA unique numbering d _i=i, wherein 1≤i≤n;

S13, from Secret Image S, take out k successively in a certain order and share the pixel of operation, note is made α _{K * 1}=(a ₁, a ₂, Λ, a _k) ^гCan be with the behavior order or classifying order as, and when number deficiency k of the pixel of sharing operation among the Secret Image S, supply by 0;

S14, utilize the RS generator matrix G that deletes code _{(k+n) * k}To α _{K * 1}Carry out encoding operation, can obtain code word β, wherein β _{(k+n) * 1}=(G _{(k+n) * k}α _{K * 1}) mod 251, preceding k the component of code word β and α _{K * 1}Identical;

S15, with last n element (b among the codeword vector β that produces _K+1, b _K+2, Λ, b _K+n) put into successively in order and gather v ₁, v ₂, Λ, v _nIn;

S16, judge whether all pixels among the Secret Image S all dispose, if, then get into step S17, otherwise, step S13 returned;

S17, choose n width of cloth image as covering image arbitrarily, will gather v ₁, v ₂, Λ, v _nIn data be embedded into the n width of cloth respectively and cover in the image, obtain final n width of cloth shadow image Y ₁, Y ₂, Λ, Y _nThe n width of cloth of choosing covers image and Secret Image S has same type and size.The last d position of the n width of cloth being covered each pixel value of image hollows out, and wherein d=8/k then rounds up when d is non-integer, forms d position default map.Because a width of cloth digital picture all is made up of pixel value, the last d place value of each pixel value is removed and when forming d position default map, when d＜4, visually be difficult to find out variation.To gather v ₁, v ₂, Λ, v _nIn data be embedded into the n width of cloth respectively and cover the default part of image, be about to gather V ₁In data embed the default part cover image 1, form shadow image Y ₁, by that analogy.When embedding, each data is divided into several parts in the default position of respectively covering image,,, then need data be split as 4 parts and be embedded into respectively in a certain 4 default positions of covering image if d is 2 o'clock as 73 being 01001001.

Secret Image that will be to be shared through above step is embedded into fully and covers in the image, forms n width of cloth shadow image, and can destroy former Secret Image this moment.

After using above-mentioned digital picture secret sharing method to share Secret Image; The present invention also provides a kind of secret restoration methods of digital picture that the Secret Image of sharing is recovered; This Secret Image forms the shadow image after embedding and covering image; Use at least k shadow image can recover the former Secret Image of sharing (when the quantity of shadow image then can not recover the former Secret Image of sharing during less than k); Wherein 2≤k≤n specifies the secret restoration methods of digital picture of the present invention below in conjunction with Fig. 2.

Fig. 2 is the process flow diagram of the embodiment of the secret restoration methods of digital picture of the present invention, specifically comprises following steps:

The S set of S21, a sky of structure;

S22, from k width of cloth shadow image, extract original share data, constitute the k data sets, note is made v ' ₁, v ' ₂, Λ, v ' _k, will gather v ' ₁, v ' ₂, Λ, v ' _kNumbering note make d ' ₁, d ' ₂, Λ, d ' _k

S23, with data acquisition v ' ₁, v ' ₂, Λ, v ' _kArrange according to numbering order from small to large, the share data note after arranging is again made v ₁, v ₂, Λ, v _k, the corresponding numbering note in ordering back is made d ₁, d ₂, Λ, d _k

S24, matrix D of structure ' _{K * k}, with the delete code d of generator matrix G of RS _iThe row assignment is given D ' _{K * k}I capable, 1≤i≤n wherein;

S25, with matrix D ' _{K * k}Carry out 251 modular arithmetic after inverting and obtain check matrix D _{K * k}

S26, respectively from each share data acquisition v ₁, v ₂, Λ, v _kIn take out a numerical value in order, arrange to constitute vectorial β according to the order of sequence _{K * 1}=(b ₁, b ₂, Λ, b _k);

S27, α=(D β) mod 251, note is made α _{K * 1}=(a ₁, a ₂, Λ, a _k);

K element (a among S28, the vectorial α that will calculate ₁, a ₂, Λ, a _k) put into S set in order, this order is corresponding with the order of taking-up pixel among the digital picture secret sharing method S13, if S13 takes out pixel in turn by behavior, then k element is put into S set by the behavior order here;

S29, judgement share data acquisition v ₁, v ₂, Λ, v _kIn all data whether all dispose, if, then get into step S30, if not, then return step S26;

S30, the former Secret Image file shared of S set for recovering to obtain.

Certainly, just list above to have lifted and utilize k shadow image to recover the method for Secret Image, when shadow picture number during greater than k, identical method also capable of using is recovered.

Embodiment 1

If the quantity L of the pixel of Secret Image to be stored is 18, image pixel value is 8 bits, so the pixel value scope of each pixel is 0～255.If the pixel value of each pixel of Secret Image S to be covered is following:

3	10	15	60	20	36	60	3	70
									30	78	90	66	99	160	15	254	10

Choose image that the n=5 width of cloth and Secret Image S have same type (being jpeg like image type) and a size arbitrarily as covering image, make and to recover Secret Image file originally when obtaining k=3 width of cloth shadow image.

Utilize digital picture secret sharing method of the present invention that the Secret Image of 18 pixels is embedded into 5 width of cloth and cover in the image, implementation method is following:

(1) by the k of image secret sharing thresholding, n value, the structure RS generator matrix G that deletes code _{(k+n) * k}, i.e. G _{(3+5) * 3}, delete code preceding 3 behaviors, one unit matrix of generator matrix, then 5 behaviors, one vandermonde determinant of RS wherein.By k=3, n=5 confirms that this RS generator matrix that deletes code is:

$G_{(3+5)\×3}=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\\ 1^0& 2^0& 3^0\\ 1^1& 2^1& 3^1\\ 1^2& 2^2& 3^2\\ 1^3& 2^3& 3^3\\ 1^4& 2^4& 3^4\end{array}\right];$

(2) 5 set of initialization v ₁, v ₂, Λ v ₅, it is empty being about to these 5 aggregate assignments;

(3) take out 3 pixel values of sharing with the behavior order from Secret Image,, be designated as as 3,10,15 ${\mathrm{\α}}_{3\×1}=\left[\begin{array}{c}3\\ 10\\ 15\end{array}\right],$ Certainly, also can classify order as;

(4) utilize RS to delete code generator matrix to array of pixel values α _{3 * 1}Carry out encoding operation and generate β _{(3+5) * 1}, promptly

${\mathrm{\β}}_{(3+5)\×1}=(G_{(3+5)\×3}\·{\mathrm{\α}}_{3\×1})\mathrm{mod}251=\left[\begin{array}{c}3\\ 10\\ 15\\ 28\\ 68\\ 178\\ 237\\ 123\end{array}\right];$

(5) remove 3 elements identical in front, last 5 elements of the code word β that produces are put into initialized 5 set v successively with α ₁, v ₂, Λ v ₅In, i.e. v ₁=28, v ₂=68, v ₃=178, v ₄=237, v ₅=123;

(6) repeating step 3 to 5, and all pixels in Secret Image all dispose, and last pixel is 15,254,10 in the present embodiment.Each gathers v like this ₁, v ₂, Λ v ₅In all contain L/3=6 element value;

(7) choose the image V ' that 5 width of cloth have vision content at random and have same type and size with Secret Image arbitrarily ₁, V ' ₂, Λ V ' ₅As covering image, last with each pixel value in this 5 width of cloth image

Position (number that rounds up is 3) hollows out, and forms d position default map.With 5 set v ₁, v ₂, Λ v ₅Interior element embeds the default part that 5 width of cloth are covered image successively, is about to v _iElement insert and cover image V ' _i3 default parts in, by that analogy, so obtain 5 width of cloth shadow image Y ₁, Y ₂Λ Y ₅At last former Secret Image is destroyed.

Introduce the method for using k=3 width of cloth shadow image that the former Secret Image of sharing is recovered below, suppose remaining shadow image Y ₁, Y ₂, Y ₃:

(1) S set of a sky of structure;

(2) from 3 width of cloth shadow images, take out primitive element successively, obtain share data acquisition v ₁, v ₂, v ₃Be about to shadow image Y ₁In element store into the set v ₁, with shadow image Y ₂In element store v into ₂In, with shadow image Y ₃In element store into the set v ₃In, each gathers v ₁, v ₂, v ₃In all contain 6 element values;

(3) come structural matrix D ' according to the numbering of shadow image _{K * k}, promptly In the present embodiment shadow image be numbered 1,2,3, then the capable assignment of 3+1 of generator matrix G is given

The 1st the row, the capable assignment of 3+2 of generator matrix G is given

The 2nd the row, the capable assignment of 3+3 of generator matrix G is given

The 3rd the row, obtain matrix $D_{3\×3}^{\′}=\left[\begin{array}{ccc}{1}^0& 2^0& 3^0\\ 1^1& 2^1& 3^1\\ 1^2& 2^2& 3^3\end{array}\right].$ Ask matrix D ' _{3 * 3}The inverse matrix of modular arithmetic (mod 251) obtains $D_{3\×3}=\left[\begin{array}{ccc}3& 123& 126\\ 248& 4& 250\\ 1& 124& 126\end{array}\right];$

(4) successively from share data acquisition v ₁, v ₂, v ₃In take out an element, promptly 28,68,178, obtain vector ${\mathrm{\β}}_{3\×1}=\left[\begin{array}{c}28\\ 68\\ 178\end{array}\right];$

(5) ${\mathrm{\α}}_{3\×1}=(D_{3\×3}\×{\mathrm{\β}}_{3\×1})\mathrm{Mod}251=\left[\begin{array}{c}3\\ 10\\ 15\end{array}\right],$ Be the pixel value of corresponding original Secret Image;

(6) with vector value α _{3 * 1}Put into S set successively with the behavior order;

(7) repeating step 4 is finished by calculating up to all data to step 6.

S set is the former Secret Image file of sharing that recovery obtains.

More than introduce digital picture secret sharing method, Secret Image has been broken to cover in the image, introduced the secret restoration methods of digital picture that the Secret Image that will share is recovered simultaneously.But the present invention is not limited to above embodiment, does not anyly break away from technical scheme of the present invention, promptly only it is carried out improvement or the change that those of ordinary skills knew, all belongs within protection scope of the present invention.

Claims (8)

1. digital picture secret sharing method breaks Secret Image to and to cover in the image, it is characterized in that said digital picture secret sharing method comprises the steps:

(1) according to the k of image secret sharing thresholding, n value, the structure RS generator matrix G that deletes code _{(k+n) * k}

(2) initialization n set v ₁, v ₂, Λ, v _n, give set v simultaneously _iA unique numbering d _i=i, wherein 1≤i≤n;

(3) from Secret Image S, take out k successively in a certain order and share the pixel of operation, note is made α _{K * 1}=(a ₁, a ₂, Λ, α _k) ^Γ

(4) utilize the RS generator matrix G that deletes code _{(k+n) * k}To α _{K * 1}Carry out encoding operation, can obtain code word β, β _{(k+n) * 1}=(G _{(k+n) k}α _{K * 1}) mod 251.

(5) with last n element (b among the codeword vector β that produces _K+1, b _K+2, Λ, b _K+n) put into successively in order and gather v ₁, v ₂, Λ, v _nIn;

(6) judge whether all pixels among the Secret Image S all dispose, if, then get into step (7), otherwise, step (3) returned;

(7) choose n width of cloth image as covering image, will gather v ₁, v ₂, Λ, v _nIn data be embedded into the n width of cloth respectively and cover in the image, obtain final n width of cloth shadow image Y ₁, Y ₂, Λ, Y _n

2. digital picture secret sharing method according to claim 1 is characterized in that, the said RS generator matrix G that deletes code _{(k+n) * k}Preceding k behavior one unit matrix, back n behavior one vandermonde determinant.

3. digital picture secret sharing method according to claim 1 is characterized in that, said step (3) can behavior be taken out the individual pixel of operation of sharing of k in proper order or to classify order as successively from Secret Image S.

4. digital picture secret sharing method according to claim 3 is characterized in that, when number deficiency k of the pixel of sharing operation among the Secret Image S, supplies by 0 in the said step (3).

5. according to the arbitrary described digital picture secret sharing method of claim 1～4, it is characterized in that the n width of cloth that said step (7) is chosen covers image and Secret Image S has same type and size.

6. digital picture secret sharing method according to claim 5 is characterized in that, the last d position that said step (7) is covered the n width of cloth each pixel value of image hollows out, and wherein d=8/k then rounds up when d is non-integer, forms d position default map, will gather v ₁, v ₂, Λ, v _nIn data be embedded into the n width of cloth respectively and cover the default part of image.

7. digital picture secret sharing method according to claim 6 is characterized in that, after step (7) forms n width of cloth shadow image, can former Secret Image file be destroyed.

8. the secret restoration methods of digital picture recovered of the Secret Image that the described digital picture secret sharing of claim 1 method is shared; Said Secret Image forms the shadow image after embedding and covering image; Using at least, k shadow image can recover the former Secret Image of sharing; It is characterized in that the secret restoration methods of said digital picture comprises the steps:

(1) S set of a sky of structure;

(2) from k width of cloth shadow image, extract original share data, constitute the k data sets, note is made v ' ₁, v ' ₂, Λ, v ' _n, will gather v ' ₁, v ' ₂, Λ, v ' _kNumbering note make d ' ₁, d ' ₂, Λ, d ' _k

(3) with data acquisition v ' ₁, v ' ₂, Λ, v ' _kArrange according to numbering order from small to large, the share data note after arranging is again made v ₁, v ₂, Λ, v _k, the corresponding numbering note in ordering back is made d ₁, d ₂, Λ, d _k

(4) matrix D of structure ' _{K * k}, with the delete code d of generator matrix G of RS _iThe row assignment is given D ' _{K * k}I capable, 1≤i≤n wherein;

(5) with matrix D ' _{K * k}Carry out 251 modular arithmetic after inverting and obtain check matrix D _{K * k}

(6) respectively from each share data acquisition v ₁, v ₂, Λ, v _kIn take out a numerical value in order, arrange to constitute vectorial β according to the order of sequence _{K * 1}=(b ₁, b ₂, Λ, b _k);

(7) α=(D β) mod 251, note is made α _{K * 1}=(a ₁, a ₂, Λ, a _k);

K element (a among the vectorial α that (8) will calculate ₁, a ₂, Λ, a _k) put into S set in order;

(9) judge share data acquisition v ₁, v ₂, Λ, v _kIn all data whether all dispose, if, then get into step (10), if not, then return step (6);

(10) the former Secret Image file shared of S set for recovering to obtain.

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